I was running out of space on one drive so I decided to move my Cygwin installation to another drive.

It turned out not to be too difficult thanks to this article Hints for Setting up Cygwin.  This is how I did it though there might be a simpler way.

1. In a bash shell save the mount points as a batch script.

   $ mount -m > /c/cygwin-mount.bat

2. Close the bash shell.
3. Move the cygwin folder from one drive to the other.  In my case that was from C:\cygwin to D:\cygwin.
4. Update all the short cuts for Cygwin in the Start Menu to use the new drive.
5. Update  cygwin.bat, which is in the top level of your Cygwin installation, to use the new drive.
6. Update your Windows environment variable to use the new Cygwin bin path, e.g. D:\cygwin\bin.
7. Open a DOS cmd prompt.  Run umount to unmount the old Cygwin mounts.

   > umount

8. Next run the mount points script.

   > C:\cygwin-mount.bat

9. Open a Cygwin bash shell to make sure everything is working correctly.